Temporal Data Modeling and Reasoning for Information Systems

Temporal knowledge representation and reasoning is a major research field in Artificial Intelligence, in Database Systems, and in Web and Semantic Web research. The ability to model and process time and calendar data is essential for many applications like appointment scheduling, planning, Web services, temporal and active database systems, adaptive Web applications, and mobile computing applications. This article aims at three complementary goals. First, to provide with a general background in temporal data modeling and reasoning approaches. Second, to serve as an orientation guide for further specific reading. Third, to point to new application fields and research perspectives on temporal knowledge representation and reasoning in the Web and Semantic Web

Temporalized logics and automata for time granularity

Suitable extensions of the monadic second-order theory of k successors have been proposed in the literature to capture the notion of time granularity. In this paper, we provide the monadic second-order theories of downward unbounded layered structures, which are infinitely refinable structures consisting of a coarsest domain and an infinite number of finer and finer domains, and of upward unbounded layered structures, which consist of a finest domain and an infinite number of coarser and coarser domains, with expressively complete and elementarily decidable temporal logic counterparts. We obtain such a result in two steps. First, we define a new class of combined automata, called temporalized automata, which can be proved to be the automata-theoretic counterpart of temporalized logics, and show that relevant properties, such as closure under Boolean operations, decidability, and expressive equivalence with respect to temporal logics, transfer from component automata to temporalized ones. Then, we exploit the correspondence between temporalized logics and automata to reduce the task of finding the temporal logic counterparts of the given theories of time granularity to the easier one of finding temporalized automata counterparts of them.Comment: Journal: Theory and Practice of Logic Programming Journal Acronym: TPLP Category: Paper for Special Issue (Verification and Computational Logic) Submitted: 18 March 2002, revised: 14 Januari 2003, accepted: 5 September 200

A timeband framework for modelling real-time systems

Complex real-time systems must integrate physical processes with digital control, human operation and organisational structures. New scientific foundations are required for specifying, designing and implementing these systems. One key challenge is to cope with the wide range of time scales and dynamics inherent in such systems. To exploit the unique properties of time, with the aim of producing more dependable computer-based systems, it is desirable to explicitly identify distinct time bands in which the system is situated. Such a framework enables the temporal properties and associated dynamic behaviour of existing systems to be described and the requirements for new or modified systems to be specified. A system model based on a finite set of distinct time bands is motivated and developed in this paper

On Relaxing Metric Information in Linear Temporal Logic

Metric LTL formulas rely on the next operator to encode time distances, whereas qualitative LTL formulas use only the until operator. This paper shows how to transform any metric LTL formula M into a qualitative formula Q, such that Q is satisfiable if and only if M is satisfiable over words with variability bounded with respect to the largest distances used in M (i.e., occurrences of next), but the size of Q is independent of such distances. Besides the theoretical interest, this result can help simplify the verification of systems with time-granularity heterogeneity, where large distances are required to express the coarse-grain dynamics in terms of fine-grain time units.Comment: Minor change

Non-null Infinitesimal Micro-steps: a Metric Temporal Logic Approach

Many systems include components interacting with each other that evolve with possibly very different speeds. To deal with this situation many formal models adopt the abstraction of "zero-time transitions", which do not consume time. These however have several drawbacks in terms of naturalness and logic consistency, as a system is modeled to be in different states at the same time. We propose a novel approach that exploits concepts from non-standard analysis to introduce a notion of micro- and macro-steps in an extension of the TRIO metric temporal logic, called X-TRIO. We use X-TRIO to provide a formal semantics and an automated verification technique to Stateflow-like notations used in the design of flexible manufacturing systems.Comment: 20 pages, 2 figures, submitted to the conference "FORMATS: Formal Modelling and Analysis of Timed Systems" 201

Deriving specifications of control programs for cyber physical systems

Cyber Physical Systems (CPS) exist in a physical environment and comprise both physical components and a control program. Physical components are inherently liable to failure and yet an overall CPS is required to operate safely, reliably and cost effectively. This paper proposes a framework for deriving the specification of the software control component of a CPS from an understanding of the behaviour required of the overall system in its physical environment. The two key elements of this framework are (i) an extension to the use of rely/guarantee conditions to allow specifications to be obtained systematically from requirements (as expressed in terms of the required behaviour in the environment) and nested assumptions (about the physical components of the CPS); and (ii) the use of time bands to record the temporal properties required of the CPS at a number of different granularities. The key contribution is in combining these ideas; using time bands overcomes a significant drawback in earlier work. The paper also addresses the means by which the reliability of a CPS can be addressed by challenging each rely condition in the derived specification and, where appropriate, improve robustness and/or define weaker guarantees that can be delivered with respect to the corresponding weaker rely conditions

Aspects of dealing with imperfect data in temporal databases

In reality, some objects or concepts have properties with a time-variant or time-related nature. Modelling these kinds of objects or concepts in a (relational) database schema is possible, but time-variant and time-related attributes have an impact on the consistency of the entire database. Therefore, temporal database models have been proposed to deal with this. Time itself can be at the source of imprecision, vagueness and uncertainty, since existing time measuring devices are inherently imperfect. Accordingly, human beings manage time using temporal indications and temporal notions, which may contain imprecision, vagueness and uncertainty. However, the imperfection in human-used temporal indications is supported by human interpretation, whereas information systems need extraordinary support for this. Several proposals for dealing with such imperfections when modelling temporal aspects exist. Some of these proposals consider the basis of the system to be the conversion of the specificity of temporal notions between used temporal expressions. Other proposals consider the temporal indications in the used temporal expressions to be the source of imperfection. In this chapter, an overview is given, concerning the basic concepts and issues related to the modelling of time as such or in (relational) database models and the imperfections that may arise during or as a result of this modelling. Next to this, a novel and currently researched technique for handling some of these imperfections is presented

Time patterns for process-aware information systems

Companies increasingly adopt process-aware information systems (PAISs) due to their promising perspectives for improved business process support. Although the proper handling of temporal constraints is crucial in this context, existing PAISs vary significantly regarding their support of the temporal perspective of a business process. To make PAISs comparable with respect to their ability to deal with temporal constraints and to facilitate the development of a time-aware PAIS, this paper suggests 10 time patterns. All patterns are based on empirical evidence we gathered in case studies. Additionally, they are validated through a systematic literature review. Based on the time patterns, we then provide an in-depth evaluation of selected PAISs and academic approaches. Altogether, the 10 time patterns will not only facilitate the selection of technologies for realizing time- and process-aware information systems but can also be used as reference for implementing time support in PAISs